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We study the coupling between backward- and forward-propagating wave modes, with the same group velocity, in a composite right- and left-handed nonlinear transmission line. Using an asymptotic multiscale expansion technique, we derive a system of two coupled nonlinear Schrödinger equations governing the evolution of the envelopes of these modes. We show that this system supports a variety of backward- and forward-propagating vector solitons of the bright-bright, bright-dark, and dark-bright type. Performing systematic numerical simulations in the framework of the original lattice that models the transmission line, we study the propagation properties of the derived vector soliton solutions. We show that all types of the predicted solitons exist, but differ on their robustness: Only bright-bright solitons propagate undistorted for long times, while the other types are less robust, featuring shorter lifetimes. In all cases, our analytical predictions are in very good agreement with the results of the simulations, at least up to times of the order of the solitons’ lifetimes.

We study the propagation of quasidiscrete microwave solitons in a nonlinear left-handed coplanar waveguide coupled with split-ring resonators. By considering the relevant transmission line analog, we derive a nonlinear lattice model which is studied analytically by means of a quasidiscrete approximation. We derive a nonlinear Schrödinger equation, and find that the system supports bright envelope soliton solutions in a relatively wide subinterval of the left-handed frequency band. We perform systematic numerical simulations, in the framework of the nonlinear lattice model, to study the propagation properties of the quasidiscrete microwave solitons. Our numerical findings are in good agreement with the analytical predictions, and suggest that the predicted structures are quite robust and may be observed in experiments.